Accelerating Precursory Activity within a Class of Earthquake Analogue Automata (original) (raw)
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Fractal features of the earthquake phenomenon and a simple mechanical model
Journal of Geophysical Research, 1991
A simplified two-dimensional stick-slip model is introduced. The system shows a kind of dynamical order-disorder phase transition with a control l•r&meter proportional to the strength of interaction. At the critical point, this model is consistent with the empirical laws of earthquakes such as Gutenberg-Richter's law, the spatial distribution of hypocenters, and the correlation function of the occurrence of earthqu&kes as results of a dynamical critical phenomenon. This model can naturally explain the locality that 1ocM magni{ude distributions often deviate from Gutenberg-Richter's law. earthquakes follows the power law relationship C(l')cx:l '(-p) . These features are very interesting and raise the question of why the earthquake phenomenon is so rich in scale invariance. In this paper we try to answer this question by analyzing a simple two-dimensional dynamical model.
What criticality in cellular automata models of earthquakes?
Geophysical Journal International, 2002
Six different 2-D prototype cellular automata models are developed to analyse the main variants of the massless automata proposed so far to reproduce earthquake physics. The analysis aims at identifying the existence of features common to these models, if any. The different model variants were studied with regard to: (1) initial grid configuration, homogeneous or random heterogeneous; (2) loading function, random or uniform; (3) local dissipation; (4) local redistribution. As a first general result, it is found that the models exhibit criticality over a very restricted range of spatial scales, much smaller than that imposed by the geometrical dimensions of the grid alone. The latter, in contrast, governs the initial transient dynamics, which exhibits much larger events. As a second general result, the foreshocks are found to increase systematically in both rate of occurrence and size prior to main shocks, with a simultaneous progressive deficit of small events. This, in turn, implies an increase in correlation length and a 'precursor' decrease in the b-value. As a third general result, the presence of foreshocks in cellular automata and the difficulties in detecting them in real earthquakes still only give a limited applicability of the present cellular automata models to the real world. As a final general result, periodic recurrence of main shocks is found only for locally dissipative models.
Microscopic and Macroscopic Simulation: Towards Predictive Modelling of the Earthquake Process, 2000
The evolution of event time and size statistics in two heterogeneous cellular automaton models of earthquake behavior are studied and compared to the evolution of these quantities during observed periods of accelerating seismic energy release prior to large earthquakes. The two automata have different nearest neighbor laws, one of which produces self-organized critical (SOC) behavior (PSD model) and the other which produces quasi-periodic large events (crack model). In the PSD model periods of accelerating energy release before large events are rare. In the crack model, many large events are preceded by periods of accelerating energy release. When compared to randomized event catalogs, accelerating energy release before large events occurs more often than random in the crack model but less often than random in the PSD model; it is easier to tell the crack and PSD model results apart from each other than to tell either model apart from a random catalog. The evolution of event sizes during the accelerating energy release sequences in all models is compared to that of observed sequences. The accelerating energy release sequences in the crack model consist of an increase in the rate of events of all sizes, consistent with observations from a small number of natural cases, however inconsistent with a larger number of cases in which there is an increase in the rate of only moderate-sized events. On average, no increase in the rate of events of any size is seen before large events in the PSD model.
Scaling in a cellular automaton model of earthquake faults
Arxiv preprint cond-mat/ …, 2000
We present theoretical arguments and simulation data indicating that the scaling of earthquake events in models of faults with long-range stress transfer is composed of at least three distinct regions. These regions correspond to three classes of earthquakes with different underlying physical mechanisms. In addition to the events that exhibit scaling, there are larger "breakout" events that are not on the scaling plot. We discuss the interpretation of these events as fluctuations in the vicinity of a spinodal critical point.
Earthquakes as a self-organized critical phenomenon
Journal of Geophysical Research, 1989
The Gutenberg-Richter power law distribution for energy released at earthquakes can be understood as a consequence of the earth crust being in a self-organized critical state. A simple cellular automaton stick-slip type model yields D(E) • E-• with r = 1.0 and r = 1.35 in two and three dimensions, respectively. The size of earthquakes is unpredictable since the evolution of an earthquake depends crucially on minor details of the crust.
A minimalist model of characteristic earthquakes
Nonlinear Processes in Geophysics, 2002
In a spirit akin to the sandpile model of selforganized criticality, we present a simple statistical model of the cellular-automaton type which simulates the role of an asperity in the dynamics of a one-dimensional fault. This model produces an earthquake spectrum similar to the characteristic-earthquake behaviour of some seismic faults. This model, that has no parameter, is amenable to an algebraic description as a Markov Chain. This possibility illuminates some important results, obtained by Monte Carlo simulations, such as the earthquake size-frequency relation and the recurrence time of the characteristic earthquake.
Recurrence Interval Statistics of Cellular Automaton Seismicity Models
Pure and Applied Geophysics, 2006
The recurrence interval statistics for regional seismicity follows a universal distribution function, independent of the tectonic setting or average rate of activity . The universal function is a modified gamma distribution with power-law scaling of recurrence intervals shorter than the average rate of activity and exponential decay for larger intervals. We employ the method of CORRAL (2004) to examine the recurrence statistics of a range of cellular automaton earthquake models. The majority of models has an exponential distribution of recurrence intervals, the same as that of a Poisson process. One model, the Olami-Feder-Christensen automaton, has recurrence statistics consistent with regional seismicity for a certain range of the conservation parameter of that model. For conservation parameters in this range, the event size statistics are also consistent with regional seismicity. Models whose dynamics are dominated by characteristic earthquakes do not appear to display universality of recurrence statistics.
Scaling in a cellular automaton model of earthquake faults with long-range stress transfer
2006
We present simulation data indicating that the scaling of earthquake events in models of faults with long-range stress transfer is composed of at least three distinct regions, corresponding to earthquakes with different underlying physical mechanisms. We discuss the interpretation of these events as fluctuations in the vicinity of a spinodal critical point. In addition to the scaling events, there are
Journal of Geophysical Research, 2000
We investigate the relationship between the size distribution of earthquake rupture area and the underlying elastic potential energy distribution in a cellular automaton model for earthquake dynamics. The frequency-rupture area distribution has the form n(S)-S'exp(-S?So) and the s. ystem potential energy distribution from the elastic Hamiltonian has the form n(E)-EVexp(-EA)), both gamma distributions. Here n(S) reduces to the Gutenberg-Richter frequency-magnitude law, with slope b-'r, in the limit that the correlation length •, related to the characteristic source size So, tends to infinity. The form of the energy distribution is consistent with a statistical mechanical mo_del with I degrees of freedom, where v=(/-2)/2 and 0 is proportional to the mean energy per site E. We examine the effect of the local energy conservation factor • and the degree of material heterogeneity (quenched disorder) on the distribution parameters, which vary systematically with the controlling variables. The inferred correlation length increases systematically with increasing material homogeneity and with increasing •. The thermal parame_.ter 0 varies systematically between the leaf springs and the connecting springs, and is proportional to E as predicted. For heterogeneous faults, z-1 stays relatively constant, consistent with field observation, and So increases with increasing • or decreasing heterogeneity. In contrast, smooth faults produce a systematic decrease in z with respect to • and So remains relatively constant. For high • approximately log-periodic quanta emerge spontaneously from the dynamics in the form of modulations on the energy distribution. The output energy for both types of fault shows a transition from strongly quasi-periodic temporal fluctuations for strong dissipation, to more chaotic fluctuations for more conservative models. Only strongly heterogeneous faults show the small fluctuations in energy strictly required by models of self-organized criticality. One of the main lines of attack on this problem is the development of numerical models for earthquakes which reproduce the observed scaling properties ]. The scaling properties of such complex, nonlinear systems are "emergent" in the sense that they cannot be predicted linearly from the local physical interactions. Instead, they result from fundamental probabilistic and statistical mechanical constraints based on the cooperative response of the system for a large number of connected elements. One of the properties of this class of discrete numerical models, consistent with analytical theories discussed in section 2, is the emergence and maintenance of broad-bandwidth scale invariance in space and time .